# If two events are complementary, are they mutually exclusive too?

May 6, 2017

Yes

#### Explanation:

By definition the complement is defined as

$\frac{B}{A} = \left\{x \setminus \in B | x \setminus \notin A\right\}$, thus by definition to be a compliment its items can only exist in one or the other but not both.